%I A002249
%S A002249 2,1,3,5,1,11,9,13,31,5,57,67,47,181,87,275,449,101,999,797,
%T A002249 1201,2795,393,5197,5983,4411,16377,7555,25199,40309,10089,
%U A002249 90707,70529,110885,251943,30173,473713,534059,413367,1481485
%V A002249 2,1,-3,-5,1,11,9,-13,-31,-5,57,67,-47,-181,-87,275,449,-101,-999,-797,
%W A002249 1201,2795,393,-5197,-5983,4411,16377,7555,-25199,-40309,10089,
%X A002249 90707,70529,-110885,-251943,-30173,473713,534059,-413367,-1481485
%N A002249 a(n)=a(n-1)-2*a(n-2).
%C A002249 4*2^n = A002249(n)^2+7*A001607(n)^2. See A077020, A077021.
%F A002249 G.f.: (2-x)/(1-x+2x^2). - Michael Somos, Oct 18, 2002
%F A002249 a(n) = trace(A^n) for the square matrix A=[1, -2;1, 0]. - Paul Barry 
               (pbarry(AT)wit.ie), Sep 05 2003
%F A002249 a(n)=2^((n+2)/2)cos(-n*acot(sqrt(7)/7)) - Paul Barry (pbarry(AT)wit.ie), 
               Sep 06 2003
%p A002249 A002249 := proc(n) option remember; >if n = 1 then 1 elif n = 2 then 
               -3 else A002249(n-1>)-2*A002249(n-2); fi; end;
%o A002249 (PARI) a(n)=if(n<0,0,polsym(2-x+x^2,n)[n+1])
%o A002249 (PARI) a(n)=if(n<0,0,2*real(((1+quadgen(-28))/2)^n))
%o A002249 (Other) sage: [lucas_number2(n,1,2) for n in xrange(0, 40)]# [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2009]
%Y A002249 Cf. A014551.
%Y A002249 Sequence in context: A120852 A058168 A058169 this_sequence A157127 A066748 
               A106583
%Y A002249 Adjacent sequences: A002246 A002247 A002248 this_sequence A002250 A002251 
               A002252
%K A002249 sign,easy
%O A002249 0,1
%A A002249 N. J. A. Sloane (njas(AT)research.att.com), Iwan Duursma (duursma(AT)research.att.com)